U.S. patent number 5,923,720 [Application Number 08/877,736] was granted by the patent office on 1999-07-13 for angle dispersive x-ray spectrometer.
This patent grant is currently assigned to Molecular Metrology, Inc.. Invention is credited to Scott W. Barton, Peter M. Calandra.
United States Patent |
5,923,720 |
Barton , et al. |
July 13, 1999 |
**Please see images for:
( Certificate of Correction ) ** |
Angle dispersive x-ray spectrometer
Abstract
An x-ray spectrometer is provided comprising an X-ray source, a
curved crystal monochromator which focuses a monochromatic x-ray
beam onto a sample surface, the curved crystal monochromator
comprising a shape which is substantially identical to a
logarithmic spiral, and a position-sensitive x-ray detector. A
method of measuring diffraction intensities from oriented samples
in real time including providing an x-ray spectrometer comprising
an X-ray source, a curved crystal monochromator which focuses a
monochromatic x-ray beam onto a sample surface, the curved
monochromator comprising the shape of a logarithmic spiral, and a
position-sensitive x-ray detector; and providing a
crystallographically oriented sample, exposing the sample to the
focused x-ray beam of the x-ray spectrometer; and measuring the
diffraction intensity at the position-sensitive detector.
Inventors: |
Barton; Scott W. (Newburyport,
MA), Calandra; Peter M. (Newburyport, MA) |
Assignee: |
Molecular Metrology, Inc.
(Newburyport, MA)
|
Family
ID: |
25370606 |
Appl.
No.: |
08/877,736 |
Filed: |
June 17, 1997 |
Current U.S.
Class: |
378/84;
378/83 |
Current CPC
Class: |
G01N
23/2076 (20130101); G21K 1/06 (20130101); B82Y
10/00 (20130101); G21K 1/062 (20130101) |
Current International
Class: |
G01N
23/20 (20060101); G21K 1/00 (20060101); G01N
23/207 (20060101); G21K 1/06 (20060101); G21K
001/06 () |
Field of
Search: |
;378/84,83,73,45 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Luken et al. "Growth monitoring of W/Si X-ray multilayers by X-ray
reflectivity and kinetic ellipsometry" SPIE 2253:327 (1994), no
month. .
Tsuchiya et al. "In-situ X-ray monitoring in MOVPE and feedback
grwoth of strained INGaAs". .
Picrauz et al. "Sructure and Characterization of strained-layer
superlattices" Semiconductors and Semimetal, 33:139 (1991), no
month. .
J.H. Underwood and D. Turner "Bent glass optics" SPIE, 106:125
(1977), no month. .
R.P. Mason and M.W. Trumbore "Differential membrane interactions of
calcium channel blockers" Biochemical Pharmacology 51:653 (1996),
no month. .
P.M. DeWolff "Multiple Guinier camera with adjustable curved
crystal monochromator" in Selected Topics on X-Ray Crystallography,
Ch. 3, ed. J. Bouman (North-Holland, Amsterdam, 1951), no month.
.
Shenfil et al. "A point focusing X-ray monochromator for the study
of low angle diffraction" J. Appl. Physics 23(8):854 (1952), no
month..
|
Primary Examiner: Porta; David P.
Attorney, Agent or Firm: Choate, Hall & Stewart
Claims
What is claimed is:
1. An x-ray spectrometer, comprising:
an X-ray source;
a curved crystal monochromator which focuses a monochromatic x-ray
beam onto a sample surface, the curved crystal monochromator
comprising a shape which is substantially identical to a
logarithmic spiral and having a width that is tapered along the
arclength s of the crystal; and
a position-sensitive x-ray detector.
2. The x-ray spectrophotometer of claim 1, wherein the size of the
focus of the x-ray beam onto the sample surface is less than or
equal to about 3.1 microns.
3. The x-ray spectrometer of claim 1, wherein the curved crystal
monochromator has a taper selected to minimize a third order
difference in arclength s between an ideal logarithmic curve and
the curved crystal.
4. The x-ray spectrophotometer of claim 1, wherein the size of the
focus of the x-ray beam onto the sample surface is less than 20
microns.
5. The x-ray spectrometer of claim 1, monochromator crystal wherein
the taper is less than about 100 milliradians.
6. The x-ray spectrometer of claim 1, wherein a linear
position-sensitive proportional detector is used.
7. The x-ray spectrometer of claim 1, wherein the monochromator
comprises a single crystal selected from the group consisting of
germanium, silicon and lithium fluoride and multilayers
thereof.
8. The x-ray spectrometer of claim 1, wherein a linear photodiode
array is used.
9. The x-ray spectrometer of claim 1, wherein a linear charge
coupled device is used.
10. The x-ray spectrometer of claim 1, wherein a 2-dimensional
proportional x-ray detector is used.
11. The x-ray spectrometer of claim 1, wherein a 2-dimensional
charge coupled device is used.
12. The x-ray spectrometer of claim 1, further comprising:
at least one single slit positioned between the source and the
monochromator.
13. The x-ray spectrometer of claim 12, wherein a plurality of
slits are positioned in front of the monochromator.
14. The x-ray spectrometer of claim 1, wherein the taper is a
linear taper.
15. A curved crystal monochromator which focuses a monochromatic
x-ray beam onto a sample surface, wherein the width of the curved
crystal monochromator is linearly tapered along an arclength s of
the crystal.
16. The monochromator of claim 15, wherein the curved crystal
monochromator has a taper selected to minimize a third order
difference in arclength s between an ideal spiral curve and the
curved crystal.
17. The monochromator of claim 15, wherein the monochromator
crystal taper is less than about 20 milliradians.
18. A method for measuring electron density in a lipid layer,
comprising:
providing an x-ray source comprising an x-ray source, a curved
crystal monochromator which focuses a monochromatic x-ray beam onto
a sample surface, the curved monochromator comprising the shape of
a logarithmic spiral and having a width that is tapered along the
arclength s of the crystal, and a position-sensitive x-ray
detector;
providing a sample comprising a single of multilamellar lipid layer
deposited on a flat substrate; and
exposing the sampler to the focused x-ray beam of the x-ray
spectrometer.
19. The method of claim 18, wherein the sample comprises natural or
synthetic lipids.
20. The method of claim 18, wherein the sample comprises natural or
synthetic lipids deposited by centrifugation from solution or
suspension.
21. The method of claim 18, wherein the sample comprises a lipid
deposited by Langmuir-Blodgett deposition.
22. The method of claim 18, wherein the sample comprises a lipid
deposited by self-assembly from solution.
23. The x-ray spectrometer of claim 1, further comprising a
sample.
24. The x-ray spectrometer of claim 1, wherein the sample comprises
an epitaxially grown layer.
25. The x-ray spectrometer of claim 1, wherein the sample comprises
a evaporated layer.
26. The x-ray spectrometer of claim 1, wherein the sample comprises
an epitaxially grown multilayer or superlattice.
27. The x-ray spectrometer of claim 1, wherein the sample comprises
a multilayer deposited by evaporation.
28. The x-ray spectrometer of claim 1, wherein the spectrometer is
attached as an accessory to a larger film deposition system.
29. The x-ray spectrometer of claim 28, wherein the film parameters
determined by the spectrometer may be used to control the
deposition of a film.
30. The x-ray spectrometer of claim 1, wherein the spectrometer is
oriented to measure x-ray reflectivity from horizontal
surfaces.
31. The x-ray spectrometer of claim 1, wherein the spectrometer is
adapted for scanning in the lateral direction.
32. The x-ray spectrometer of claim 1, further comprising:
a second focusing device positioned so as to focus in the plane
substantially perpendicular to the curved crystal
monochromator.
33. The x-ray spectrometer of claim 32, wherein the second focusing
device comprises a curved mirror.
34. The x-ray spectrometer of claim 32, wherein the second focusing
device comprises a curved crystal monochromator.
35. A method of measuring diffraction intensities from oriented
samples in real time, comprising;
providing an x-ray spectrometer comprising an x-ray source, a
curved crystal monochromator which focuses a monochromatic x-ray
beam onto a sample surface, the curved monochromator comprising the
shape of a logarithmic spiral and having a width that is tapered
along the arclength s of the crystal, and a position-sensitive
x-ray detector; and
providing a crystallographically oriented sample;
exposing the sample to the focused beam of the x-ray spectrometer;
and
measuring the diffraction intensity at the position-sensitive
detector.
36. The method of claim 18 or 35, wherein the taper is a linear
taper.
Description
BACKGROUND OF THE INVENTION
1. Field of Invention
The present invention is directed toward the field of x-ray
diffraction as a versatile tool to determine the structure of
atomic and superlattice systems with preferred orientation along at
least one dimension. The invention may be configured for the
determination of structure in lipid membranes, in-situ thickness
measurements of thin films during growth, and determination of
lattice mismatch in epitaxial crystalline films.
2. Description of the Prior Art
X-Ray diffraction has been used to measure in situ thickness of
thin films during deposition (Luken, et. al., SPIE Vol. 2253:327
(1994)). Luken et al. describe an angle dispersive x-ray
reflectometer which employs a Johansson-type (T. Johansson, Zeit.
Physik, 82:507 (1933)) curved crystal monochromator to focus and
wavelength-select X-radiation, with a convergence angle of
2.5.degree. (4.4.times.10.sup.-1 radians), down to a silicon
substrate surface on which a W/Si multilayer is grown. The
Johansson-type crystal is one in which the reflecting surface is
ground to a radius of curvature 2R and the crystal is subsequently
bent to a radius of curvature R. The low angle x-ray reflectivity
is monitored from the Si substrate simultaneously between 0.degree.
and 2.5.degree. using a linear position sensitive charge-coupled
device (CCD) detector. The authors used the instrument to monitor
the growth of the multilayer in-situ during evaporative
deposition.
While in principle, the Johansson crystal provides "perfect"
point-to-point focusing, there are limitations to using Johansson
crystals. For example, the size of the beam at the focus is
approximately the same size as the source. For a fine focus x-ray
source, with a target source size of 0.4.times.8 mm.sup.2, this
dimension at a 6.degree. (0.10 radians) takeoff angle is defined by
(0.4 mm)Sin(0.10) and has a value of about 42 .mu.m in the focusing
plane. To further reduce the focus, the effective source size would
need to be reduced with a slit to block part of the radiation. Not
only would the use of a slit diminish the intensity of the x-ray
beam, but alignment is now made considerably more difficult, since
the monochromator and the sample need to be positioned to within
microns with respect to the source in order to take advantage of
the small focus. Furthermore, because the crystal monochromator
surface must be ground and bent to a very specific curvature, there
is, for practical purposes, no forgiveness built into the design to
compensate for misalignments or bending error. Thus, the
requirement that the surface be ground and then bent makes the
fabrication expensive.
Small angle x-ray scattering has been used to measure structure in
oriented lipid bilayers (Mason and Trumbore, Biochemical
Pharmacology 51:653 (1996)). Using small-angle x-ray spectrometry,
Mason and Trumbore report the sensitivity of the method to indicate
the incorporation and location of antioxidants into the lipid
matrix. To achieve the orientation, multilayer stacks of the lipid
bilayers are centrifuged down onto a flat substrate from vesicles
suspended in an aqueous medium. The lipids are found to align
spontaneously with the stacking axis normal to the substrate
surface. The substrate is made from a bendable sheet of aluminum
which is subsequently mounted on a curved glass surface (radius of
curvature c.a. 20 mm). An incident x-ray beam is then focused with
a bent grazing incidence mirror to illuminate the curved substrate
with an intense beam of small, but unspecified, angular divergence.
Different parts of the incident beam intersect the curved surface
at different angles of incidence, and the scattering from the
entire beam is measured on a position-sensitive x-ray detector
which measures the intensity as a function of linear position along
the detector axis. The discrete diffraction peak intensities are
then Fourier transformed to determine the electron density profile
within the lipid bilayer. Mason and Trumbore report the difference
in electron density between the oriented lipid lamellar stack
incubated in the vesicle state without antioxidant and the same
lipid incubated with the target antioxidant in the vesicular
suspension before centrifugation.
While this method is able to capture all the relevant diffraction
information, the technique suffers from the time-consuming step of
gluing the aluminum substrate to the curved glass surface.
Furthermore, the x-ray beam is not monochromatic, but is simply
filtered to significantly reduce the K.sub..beta. radiation. The
dominant radiation which diffracts from the sample is the
K.sub..alpha.1 /K.sub..alpha.2 doublet. The continuous
brehmstrahlung background radiation, particularly at energies
between 4 and 8 keV, remains. This continuous spectrum radiation
increases the background signal on top of which the diffraction
peaks are observed and this subsequently diminishes the ability to
observe weak diffraction lines and accurately determine integral
peak areas.
High resolution, wide angle x-ray scattering is commonly used to
determine the lattice parameters in epitaxially grown films (in
particular, strained-layer superlattices) with respect to the
lattice of the single crystal substrate. The typical approach is to
employ a two-crystal spectrometer (monochromator and sample) and
measure a rocking curve of the sample in the vicinity of a Bragg
diffraction angle from the sample substrate. These angles are
typically in the range of 30.degree. to 50.degree. and the rocking
curve scan is performed over a range of several degrees. During the
rocking scan, the diffraction intensities are measured using a
scintillation detector with an entrance slit large enough to accept
diffraction over an angular range of several degrees. The wide
detector slit precludes the ability to know the diffraction angle
precisely. As a result, satellite peaks and orientation of
reciprocal lattice vector in strained-layer superlattices are not
readily discernible.
Picreaux et al. (Semiconductors and Semimetals, 33:139 (1991))
employ a linear position-sensitive x-ray detector (PSD) to measure
diffraction intensities from epitaxial films in rocking curve scans
with a high resolution two-crystal x-ray spectrometer. While the
use of the PSD provides information to allow reciprocal space
mapping of the epitaxial layers, the method still requires
illumination of the substrate with a highly collimated,
monochromatic beam and then measuring the diffraction intensities
while step scanning the sample tilt one angle at a time; this
approach is both complicated and time-consuming.
Using a high resolution, two-crystal x-ray spectrometer, Tsuchiya
et al. (Proc. 4th Indium Phosphide and Related Materials Conf.,
Newport, R.I., 1992) describe feedback control used to adjust the
growth conditions during deposition of a vapor phase epitaxial
grown film of InGaAs on a single crystal substrate, InP. A
scintillation detector with a wide slit was used and the entire
x-ray source and monochromator optics were rotated about the sample
in order to perform the rocking curve scans. While this method
demonstrates the feasibility of using x-ray diffraction for
deposition feedback, rotation of the x-ray source about the sample
is cumbersome and limits the amount of space available for the
deposition system. Furthermore, the method is impractical for
faster deposition, since the incident angles are stepped one at a
time.
X-rays may be simultaneously focused and monochromatized by
reflecting a divergent x-ray beam from a curved single crystal such
that incident beam intersects the crystal at the Bragg diffraction
angle for the desired wavelength. An ideal shape for such a
focusing x-ray monochromator is for the crystal curvature to be
identical with a logarithmic spiral. DeWolff (Selected Topics on
X-Ray Crystallography, Ch. 3, ed. J. Bouman, North-Holland,
Amsterdam, 1951) describes a four-point crystal bender to
approximate the ideal logarithmic spiral form for a focusing
monochromator crystal to second order with respect to the local
crystal curvature. This monochromator design has been employed for
almost half a decade in powder diffraction spectrometers. The
bending design is simple, robust, and in contrast to the
Johansson-type focusing, the logarithmic spiral does not require a
true point x-ray source.
The main disadvantage of this type of focusing monochromator is
that the focusing quality can not be improved beyond that already
accomplished with the conventional four-point bending apparatus.
This inherent limitation is due to the difference in functional
form between the ideal logarithmic spiral and the shape that the
monochromator can assume in a mechanical, four-point bending
apparatus.
X-rays are totally reflected from smooth mirror surfaces when the
x-rays illuminate the mirror below a grazing incident critical
angle. For hard x-rays (>1 keV), this angle is typically on the
order of a few tenths of a degree. Underwood and Turner (SPIE,
106:125 (1977)) describe how bent, nondiffracting mirror surfaces
can made to focus or collimate x-rays more efficiently by grinding
the sides of the mirror such that the width of the reflecting
surface varies as function of the length. This shaping procedure is
used to "tune" the moment of inertia as a function of length, and
allows a bending system to more accurately define the shape of the
mirror to the ideal parabola or ellipse. The authors intended this
design to be used in astrophysical applications for x-ray
telescopes; and these mirror focusing elements differ significantly
from diffracting crystal optics.
Thus, there remains a need for an x-ray spectrometer with a curved
crystal monochromator which can provide improved point focusing of
the x-ray source and micron scale scanning of the sample surface.
There is a further need for methods of preparing curved crystals
having a curvature of a logarithmic spiral which overcome the
inherent limitations of the prior art.
SUMMARY OF THE INVENTION
It is the object of the present invention to provide an x-ray
spectrometer which provides superior point focusing of a source
x-ray beam from a real extended source.
It is a further object of the invention to provide a curved single
crystal or other dynamically diffracting element for use as an
x-ray monochromator having a surface curvature which most nearly
approximates a logarithmic spiral. Dynamical diffraction includes
diffraction from perfect crystals, like silicon germanium and
lithium fluoride, as well a reflection from synthetic multilayers,
such as W/Si alternating film stacks.
It is yet a further object of the invention to provide an x-ray
reflectometer which permits data accumulation over a range of
angles incident to the sample surface in a single measurement.
It is yet a further object of the invention to provide a method of
measuring x-ray reflectance or x-ray diffraction over a range of
incident angles to the sample surface in a single measurement.
It is yet a further object of the present invention to provide an
improved and more efficient method of determining electron density
profiles in lipid layers.
It is yet a further object of the present invention to provide an
improved and more efficient method of determining epitaxial film
structure and growth.
These and other objects of the invention are accomplished by use of
the x-ray spectrometer described herein. Unique features of the
invention are intended to make it possible to reduce the data
collection times several orders of magnitude and perform
diffraction scanning with resolution on the order of microns in the
scanning direction.
By "logarithmic spiral", it is meant a mathematically defined
surface curvature that is often occurring in nature. Diverse
objects such as snail shells, fiddlehead ferns and other naturally
occurring elements follow the shape of the logarithmic spiral;
while the curvatures described in this disclosure are of the
logarithmic spiral form, the radius of curvature is orders of
magnitude larger than those found in nature.
An advantage of the present invention is that the x-ray source need
not be a point in order to obtain high resolution. This is an
advantage as most real laboratory x-ray sources are extended and
not point sources. In addition, due to the ability to
simultaneously collect date over a range of incident angles, data
collection is much more rapid than in conventional
spectrometers.
In one aspect of the invention, an x-ray spectrometer is provided
which includes an x-ray source; a curved crystal monochromator
which focuses a monochromatic x-ray beam onto a sample surface, the
curved crystal monochromator comprising a shape which is
substantially identical to a logarithmic spiral; and a
position-sensitive x-ray detector positioned to receive x-ray beams
diffracted or reflected from a sample surface. Whether or not the
source x-ray beam is diffracted or reflected is a function of the
angle of incidence of the x-ray beam on the sample.
In preferred embodiments, the width of the curved crystal
monochromator is linearly tapered along an arclength s of the
crystal. In other preferred embodiments, width of the the curved
crystal monochromator has a taper selected to minimize a third
order difference in s between an ideal logarithmic spiral curve and
the curved crystal. The monochromator crystal may be shaped along
its length in a form other than rectangular. The taper of the
crystal monochromator may be a taper less than about 100
milliradians and preferably about 20 milliradians.
In other preferred embodiments, a linear position-sensitive
proportional detector is used. The position-sensitive detector may
be a linear photodiode array, a linear charge coupled device, a
two-dimensional proportional x-ray detector, or a two-dimensional
charge coupled device. The spectrometer may also include at least
one single slit is positioned between the x-ray source and the
monochromator and a plurality of slits may be positioned in front
of the monochromator.
In other preferred embodiments of the invention, the x-ray
spectrometer includes a sample which may be an epitaxially grown
layer, an evaporated layer, an epitaxially grown multilayer or
superlattice, or a multilayer deposited by evaporation. The x-ray
spectrometer may be attached as an accessory to a larger film
deposition system and the film parameters determined by the
spectrometer may be used to control the deposition of a film.
In other preferred embodiments, the x-ray spectrometer may be
adapted oriented to measure x-ray reflectivity from horizontal
surfaces (i.e., liquids) or for scanning in the lateral direction.
The x-ray spectrometer may additionally include a second focusing
device, such as a curved mirror, positioned so as to focus in the
plane substantially perpendicular to the curved crystal
monochromator. The second focusing device may be a curved crystal
monochromator.
In another aspect of the invention, a curved crystal monochromator
is provided which focuses a monochromatic x-ray beam onto a sample
surface, wherein the curved crystal monochromator comprises a shape
substantially identical to a logarithmic spiral as measured along
the crystal monochromator length, wherein the width of the curved
crystal monochromator is linearly tapered along an arclength s of
the crystal. In preferred embodiments, the curved crystal
monochromator has a taper selected to minimize a third order
difference in s between an ideal logarithmic spiral curve and the
curved crystal. The monochromator crystal may be shaped along its
length in a form other than rectangular. The monochromator crystal
may have a taper less than about 0.10 radians, and preferably less
than 0.02 radians.
In another aspect of the invention, a method for measuring electron
density in a lipid layer is provided by providing an x-ray
spectrometer comprising an X-ray source; a curved crystal
monochromator which focuses a monochromatic x-ray beam onto a
sample surface, the curved monochromator comprising the shape of a
logarithmic spiral; and a position-sensitive x-ray detector; and
providing a sample comprising single or multilamellar lipid layers
deposited on a flat substrate; exposing the sample to the focused
x-ray beam of the x-ray spectrometer and measuring the diffraction
intensity at the position sensitive detector.
In preferred embodiments, the sample may be natural or synthetic
lipids, natural or synthetic lipids deposited by centrifugation
from solution or suspension, a lipid deposited by Langmuir-Blodgett
deposition, or a lipid deposited by self-assembly from
solution.
In yet another aspect of the invention, a method of measuring
diffraction intensities from oriented samples in real time is
provided by providing an x-ray spectrometer comprising an X-ray
source; a curved crystal monochromator which focuses a
monochromatic x-ray beam onto a sample surface, the curved
monochromator comprising the shape of a logarithmic spiral; and a
position-sensitive x-ray detector; and providing a
crystallographically oriented sample; exposing the sample to the
focused x-ray beam of the x-ray spectrometer; and measuring the
diffraction intensity at the position-sensitive detector.
BRIEF DESCRIPTION OF THE DRAWING
The invention is described with reference to the following Figures,
which are provided for the purposes of illustration only and which
are not intended to be limiting of the invention, and in which:
FIG. 1 is a schematic illustration of the x-ray spectrometer of the
invention;
FIG. 2 is a schematic illustration of the four-point bending
technique used to shape a curved crystal monochromator;
FIG. 3 is a plan view of a linearly tapered crystal of the
invention prior to bending;
FIG. 4 is a schematic illustration of another embodiment of the
x-ray spectrometer of the invention;
FIG. 5 is an illustration of the diffractive relationships in the
x-ray spectrometer of the invention;
FIG. 6 is an enlarged illustration of the diffractive relationships
in a portion of the x-ray spectrometer of the invention; and
FIG. 7 is an illustration of the source of the aberration error at
the focus due to the difference in direction between rays reflected
from neighboring points on the logarithmic spiral and the
corresponding real crystal.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is designed to perform angle dispersive x-ray
diffraction and is composed of several components shown in FIG. 1.
X-rays emanating from an x-ray source 10 are focused by a curved
crystal monochromator 12, with the unique design that will be
described presently below. The x-rays are focused onto a sample
specimen 14 which has a well-defined periodicity along the z-axis.
Diffracted intensities from the sample within an angular range
defined by the focus convergence are detected simultaneously at
different diffraction angles on a position-sensitive x-ray detector
16.
The x-ray sources hereinafter referred to as the "source" may be
sources well-known in the art such as sealed x-ray tubes or
rotating anodes. In x-ray laboratory sources, a common source is
CuK.sub..alpha. radiation, but the source could equally be
generated from molybdenum, silver, chromium, rhodium, iron and
other target materials. The convergence of the monochromator focus
and the focal size are dependent upon x-ray energy and also the
orientation of the reflecting atomic planes to the monochromator
surface. These features are taken into consideration in the
analysis which follows.
Position sensitive detectors which are known in the art are
suitable for use in the x-ray spectrometer of the invention.
Suitable position sensitive detectors include linear
position-sensitive proportional detectors, linear photodiode
arrays, linear charge coupled devices, two-dimensional proportional
x-ray detectors, two-dimensional charge coupled devices.
The x-ray spectrometer of the invention is useful in analyzing any
material which exhibits a well-defined periodicity along at least
one dimension. By way of example only, the sample includes natural
or synthetic lipids, epitaxially grown layers, evaporated layers,
and epitaxially grown multilayers or superlattices. The sample
surface may be a solid or a liquid; in the latter case, the sample
is horizontal within the spectrometer.
The monochromator crystal desirably is a perfect single crystal,
the exact composition of which may be chosen according to the needs
of the particular application. Single crystal germanium, silicon
and lithium fluoride are preferred single crystals for use in the
present invention. The crystal is oriented along a selected
diffraction plane; however, the particular diffraction plane is not
of great significance to the invention. Orientation of the crystal
monochromator will have an effect on the diffracting angle of the
crystal, which may be taken into consideration in the curvature of
the crystal as discussed below. In addition, it is recognized that
certain synthetic multilayers may be used in place of the perfect
crystal. These multilayers may consist of alternating thin films of
two or more materials, e.g., Si/W deposited on a thin bendable
substrate.
The monochromator with dimensions as shown in FIG. 3 is bent by a
four point bender (shown schematically in FIG. 2) to assume the
shape which substantially approximates that of a logarithmic spiral
which provides perfect focusing from an extended source. This is in
contrast to the Johansson-type monochromator (described by Luken et
al.) which requires a point source to achieve perfect focusing.
Since real laboratory x-ray sources have a finite size, the
logarithmic spiral form is better suited for laboratory
experiments.
Prior to subjecting the monochromator crystal to a four-point
bending process in order to approximate a logarithmic spiral
curvature, the sides of the monochromator crystal which define the
width are ground in order to bend the real monochromator to a shape
which significantly improves the mechanical approximation to the
ideal logarithmic spiral. The shaping introduces a taper and
preferably a linear taper along the length of the crystal. The
taper is selected commensurate with the application of the
apparatus, the composition of the crystal, the wavelength of the
x-ray and the geometry of the spectrometer; however, tapers of less
than 0.10 radians and preferably less than 0.02 radians are
typical. A crystal exhibiting an exemplary taper of the invention
is shown in FIG. 3. Referring to FIG. 3, in which the unbent, flat
crystal is shown in plain view, L is defined as the length of the
monochromator crystal, W.sub.0 is the width of the crystal at the
center line (CL) of the crystal, W.sub.1 is the width of the
crystal at its larger end and W.sub.2 is the width of the crystal
at its smaller end. For the unbent crystal shown in FIG. 3, the
width dimension of the coincident along the y-axis, the length L is
coincident along the x-axis and the thickness is coincident with
z-axis. A linear taper is defined by and angle .tau.=arctan
{(W.sub.1 -W.sub.2)/L}. These dimensions are indicated in FIG. 3.
This new design produces a beam focus which is at least an order of
magnitude smaller than that described in the prior art (de Wolff),
without a restriction in the source size; furthermore, the focus
quality of the present invention makes it possible to perform x-ray
diffraction and x-ray reflection in a high resolution scanning
mode.
The taper may be introduced into the crystal using standard crystal
handling techniques. For example, the crystal may be securely
mounted in a clamping device in a surface grinding apparatus. The
edge of the crystal is indicated with a dial indicator which is a
sensitive spring-loaded mechanical measuring tool. Such instruments
can determine the relative displacement of a surface to 0.0005"
(0.5 mil) or less. The crystal may then be tilted until the edge
has the desired relative displacement from one end to the other
corresponding to the desired taper. The taper is introduced by
applying a grinding surface such as a diamond grinding wheel across
the crystal edge. The process is then repeated on the other side of
the crystal. A camera-equipped apparatus, such as an optical
comparitor, may be used for such an operation.
For sample specimens in which diffuse scattering distorts or
prohibitively increases the background intensity relative to the
specular intensity, a single or "ladder" slit 20 can be used to
determine the integrated specular scattering above the background,
as is shown in FIG. 4. The slit 20 serves to define a beam with an
angular convergence much smaller than that defined over the entire
monochromator. The purpose is to create a highly collimated beam
which is incident on the sample at a specific angle. One would
observe on the PSD a single well-defined peak corresponding to the
specularly reflected beam. One or more slits may be employed in the
spectrometer, as needed. The method and apparatus may be adapted
for use with a solid or a liquid sample.
In addition, the spectrometer may include a second focusing device.
The second focusing device typically is positioned within the
spectrometer so as to focus in the plane substantially
perpendicular to the curved crystal monochromator. This provides
focus along a second axis resulting in a reduced spot size of the
x-ray beam. The reduced spot size makes the spectrometer well
suited for used as a diffraction microprobe. The second focusing
device may be any conventional focusing crystal or mirror. In a
preferred embodiment, it may also be a curved crystal monochromator
of the type described herein.
The log spiral (LS). The specific curvature for the LS
monochromator is determined by 1) the desired x-ray wavelength, and
2) the orientation of the crystallographic diffraction planes with
respect to the monochromator surface and 3) the
monochromator/source and monochromator/focus distances. The
important feature of the logarithmic spiral is that the angle,
.phi., formed between a vector from the origin and the tangent to
any point on the spiral curve is constant. In FIG. 5, this geometry
is realized for the present spectrophotometer by providing a
crystal monochromator having an ideal logarithmic spiral with the
origin representing a focus on a sample surface, F.sub.0. For the
general case where the diffracting crystallographic planes of the
monochromator are oriented at an angle .sigma. with respect to the
monochromator surface, the constant grazing angle of incidence is
given as:
where .theta..sub.BRAGG is the Bragg angle of diffraction for the
monochromator and .sigma. is the orientation angle of diffracting
crystallographic planes with respect to the monochromator surface,
and where the Bragg angle of the monochromator for a given
wavelength and diffraction plane is: ##EQU1## where .lambda. is the
x-ray wavelength and d is the characteristic atomic spacing between
the monochromator's diffraction plane.
For the purposes of this disclosure, a quantitative description of
the LS is presented in order to demonstrate the ability of this
invention to achieve micron scale focal dimensions. The
mathematical representation of the LS has the following form in
polar coordinates (r,.theta.) where r is the polar distance from
origin to a point on the logarithmic spiral; .theta. is the polar
angle of the logarithmic spiral; and .alpha., .beta. are
constants:
which can be written parametrically in Cartesian coordinates,
(x,y), as a function of .theta.: ##EQU2## assuming the geometry
shown in FIG. 5, with the focus placed at the origin and the center
of the crystal positioned at x=.alpha.=F.sub.0 M.sub.0 and y=0.
F.sub.0 M.sub.0 represents the distance from the center of the
monochromator crystal (M.sub.0) to the sample surface (F.sub.0).
F.sub.0 also coincides with the origin corresponding to the ideal
logarithmic spiral.
The constant .beta. is a function of the constant .phi. and
determined from the scalar product between the unit ray along
F.sub.0 M:
and the unit tangent at M where M represents an arbitrary point on
surface of the monochromator: ##EQU3## where i and jare unit
vectors in the x and y directions, respectively. Thus, ##EQU4## By
the present convention in which a clockwise rotation of .theta. is
negative, the positive value for .beta. is chosen.
Of additional relevance to this disclosure are the arclength, s,
along the logarithmic spiral axis: ##EQU5## and the radius of
curvature, R.sub.LS (.theta.):
where R.sub.LS (.theta.)is the radius of curvature at the point on
the spiral defined by .theta..
For our exemplary case of the diffractometer design, we choose a
copper x-ray source with a germanium single crystal monochromator
selecting the Cu K.sub..alpha.1 radiation (1.5407 .ANG.),
reflecting from the Ge(111) crystallographic planes. A symmetric
reflection geometry for the LS will be adopted, where
.phi.=.theta..sub.BRAGG =13.63.degree. (0.2379 radians). The
distances F.sub.0 M.sub.0 =M.sub.0 S.sub.0 as represented in FIG. 5
may be typically 165 mm. One of the advantages of the LS
monochromator is that it views an extended x-ray source, shown in
FIG. 6 as the line at S.sub.0 S.sub.1. The x-ray source size in a
conventional laboratory system is defined by the rectangular
portion of a target on which is focused an accelerated electron
beam. In a typical configuration of this invention, a Cu x-ray tube
with target dimensions 2 mm.times.12 mm may be employed. The tube
may be tilted so that the monochromator views the 2 mm dimension
from a takeoff angle of 10.degree. (0.174 radians), making the
effective source size seen by the monochromator equal to (2
mm)Sin(0.174)=0.35 mm. Based on this value, a typical 30 mm length
of the crystal will collect and reflect a fan of radiation with a
convergence angle, .omega., equal to 0.045 radians (de Wolff). The
radius of curvature of the monochromator at M.sub.0 is 700 mm. A
0.5 mm thick crystal may be used.
The x-ray focus characteristics are determined by the quality of
the match between the bent crystal and the ideal logarithmic
spiral. By using a four-point bending apparatus, de Wolff
approximated the ideal logarithmic shape to second order in s (de
Wolff) . In this invention disclosure, we describe a method by
which the logarithmic shape can be bent to a vanishingly small
third order term for the best case; and even if the best case
situation can not be met exactly, a finite but small second order
term remains, but this term is at least one order of magnitude less
than the remainder term in the prior art. It is precisely this
focusing geometry that makes micron resolution scanning possible
with our invention.
Below we demonstrate that the focus in our new monochromator design
is superior to that described in the prior art. We first describe
the radius of curvature for the longarithmic spiral monochromator
crystal (equation 10) in the form:
where ##EQU6## and R.sub.0,LS is the radius of curvature at s =0,
at the center of the crystal and A.sub.LS is the coefficient of s
in equation (11) for the radius of curvature for the logarithmic
spiral.
This curvature radius is compared to that for a four-point bender
in which two adjustable loads are applied evenly across the crystal
width and symmetric about the center line of the crystal, with two
symmetric supports across the width, but closer to the center than
where the adjustable loads are applied (see FIG. 2). The prior art
(de Wolff, Luken et al.) employ a rectangular shaped crystal
monochromator. Our invention employs a linearly tapered crystal
such that the moment of inertia I along the bending axis, x, is:
##EQU7## where w is the width of the crystal, t is the thickness
and A.sub.cryst is the slope of the taper. It is apparent that, for
the prior art crystal where the taper A.sub.cryst =0, the moment of
inertia is the same along the length of the crystal, whereas for
the crystal monochromator of the invention, the moment of inertia
varies along the axis of bending.
From elementary beam theory, the curvature of the linear taper
crystal at point x, along the bending axis bent in the described
four-point bender is: ##EQU8## where L.sub.0 is the bending moment
(the change in bending moment of inertia along the taper) at the
crystal center, E is the Young's modulus of the monochromator,
I.sub.0 is the bending moment of inertia at the crystal center, and
B.sub.cryst is the slope of the bending moment from point 2 to
point 3 in FIG. 2 introduced by unequal loading at points 1 and 4
in FIG. 2. We recognize that the curvature for the ideal LS form
(equation 11) is cast as a function of s, while the dimension, x,
described in equation 14 is measured along the axis perpendicular
to the reaction forces. The two lengths differ in third order:
##EQU9## The best match between the logarithmic spiral and the real
crystal will be given when ##EQU10## A.sub.LS, and R.sub.0,LS are
defined by .phi. and F.sub.0 M.sub.0 in equation 12. Recognizing
that the aberration error at the focus is due to the difference in
direction between rays reflected from neighboring points on the LS
and the corresponding real crystal (see FIG. 7), one can write the
integrated error for half of the monochromator .PHI. as: ##EQU11##
where it is understood that M.sub.1 is measured along the s axis,
M.sub.1 is the effective endpoint closest to the focus on the
surface of the monochromator crystal, R.sub.0 is the monochromator
crystal radius of curvature at the center of the bending axis, and
the following expansions have been used: ##EQU12## we arrive at the
significant result that ##EQU13##
Using .phi.=0.238 radians and F.sub.0 M.sub.0 =165 mm, equation 12
gives A.sub.LS =5.89E-3. With .omega.=0.045 radians, the best match
between our mechanical approximation and the ideal logarithmic
spiral curve the size of the focus is only 5E-3 microns (equation
12). Without a linear taper in the crystal monochromator width, the
focal size using the same exemplary geometry would be 20 microns
for a crystal of the same dimensions.
We recognize that, due to uncertainties in the shaping of the
monochromator taper, this ideal condition may not be met. The
uniqueness of this instrument is that the four-point bender is used
to correct for these shape errors. We shall assume that the error
can be corrected to first order by setting the unequal loads such
that A.sub.cryst -B.sub.cryst =A.sub.LS in equation 17. For this
case where the taper in the crystal deviates slightly from the
ideal case, the best focus that can be achieved is given by:
##EQU14## In practice, the major factor in deforming the quality of
the focus is due to the finite error associated with grinding the
sides of the monochromator crystal. Recognizing that A.sub.cryst is
the tangent of the convergence angle for the width of the
monochromator, a conservative estimate for the grinding precision
is on the order of 0.001 radians. Setting A.sub.cryst -A.sub.LS
=0.001, A.sub.LS =5.89E-3radians, M.sub.1 =15 mm and adjusting the
bending loads such that A.sub.cryst -B.sub.cryst =0, equation 20
and 21 defines the focus size of 3.1 microns.
Application to Lipid Membrane Structure. The invention can be used
to determine the electron density profile in lipid bilayers with
applications in the field of drug testing. Compared to the standard
methods of x-ray diffraction from bilayer stacks, the use of angle
dispersive x-ray diffraction as described herein is cost-effective,
enables faster data collection times, permits straightforward
sample preparation and may be easily adapted for batch sampling
processing for screening of a large number of samples.
Two methods are currently employed in the prior art to collect the
x-ray intensity generated by diffraction of the lipid bilayer as a
function of the scattering angle for the lamellar systems. In the
simplest case, the multilayer stacks of the lipid bilayers are
centrifuged from vesicles in an aqueous medium and spun down onto a
flat substrate; they are found to spontaneously align with the
stacking axis normal to the substrate surface. The substrate is
then mounted on a goniometer which rotates the sample to an angle
.theta. with respect a fixed x-ray beam while the reflected
intensity is collected on either a scintillation detector rotated
to angle 2.theta. with respect to the incident beam or linear
position-sensitive x-ray detector. This method has the advantage
that with monochromatization and collimation of the x-rays, high
resolution with low background allows a high quality electron
density profile to be extracted. The drawback is that the intensity
must be collected at each scattering angle individually, leading to
long collection times on the order of hours.
In the second prior art method, the sample is prepared in the same
fashion as described above; however, the substrate is made from a
bendable aluminum foil which is then mounted on a curved surface
with a radius of curvature of about 20 mm. The incident beam is
then focused with a curved grazing incidence mirror to illuminate
the curved surface with an intense beam of low angular divergence.
Different parts of the incident beam intersect the curve surface at
different angles of incidence, and the scattering from the entire
beam is measured on a position-sensitive x-ray detector. The
advantage to this arrangement is the speed and simplicity of data
collection. The entire scattering curve is collected over the
desired range of angles simultaneously without the need for
goniometer motion control. The disadvantage to this approach is
that the beam is not truly monochromatic, but composed mainly of
the K.sub..alpha.1 and K.sub..alpha.2 doublet over a background of
primarily lower energy x-rays. Scattering from the low energy x-ray
tail distribution as well as off-specular diffuse scattering
increases the background noise and can obscure weaker diffraction
lines. Furthermore, the mounting of samples is time-consuming and
subject to errors associated with buckling of the substrate during
mounting. While the position sensitive detection increases the
speed of data collection, one must also account for x-ray intensity
distributions across the beam reflected from the focusing
mirror.
The present invention provides a means of measuring electron
density in lipid bilayers that represents an improvement over the
current prior art methods. The apparatus is shown generally in FIG.
1. The instrument may be set up to illuminate a stack of lipid
bilayers centrifuged down to a flat smooth substrate (for example,
a glass slide or polished Si wafer). The lipids align with their
lamellar stacks oriented along the surface normal, creating a
system with one-dimensional ordering along the normal to the flat
substrate.
Rather than using aluminum substrates which are subsequently glued
to curved cylindrical surface as described in the prior art, the
lipids may be centrifuged down onto inexpensive glass substrates no
more than 10 mm on a side or in diameter. The entire diffraction
apparatus may then be sealed and flushed with dry helium to reduce
air scattering and attenuation of the x-ray beam. The sample may be
housed in a separate chamber which will be temperature controlled
by water circulation and through which dry He and water-saturated
He can be flowed in variable proportions to adjust the relative
humidity in the lipid matrix.
X-rays from a conventional copper x-ray tube may be simultaneously
monochromatized and focused onto a flat substrate onto which the
lipids have been deposited. The monochromator is bent to
approximate a logarithmic spiral along the bending axis according
to the methodology described hereinabove. This shape ensures that
the focus is of high quality and that the beam incident on the
sample will be only the K.sub..alpha.1 component from the Cu x-ray
tube source. The invention can measure the diffraction intensity
over a range of angles, .theta..sub.diff, simultaneously. From
previous studies of these systems, the scans need to be extended to
the range of at least 6.degree.. In certain cases, the range must
be extended by tilting the sample, while the diffraction
intensities are indexed in a storage file as a function of the
vector k, defined by: ##EQU15## The data may be indexed in the
storage file as a function of the scattering vector. As opposed to
longer date accumulation times at two or three sample angles as is
conducted in the prior art, the scanning mode ensures that each
resolution element within the fan of radiation is used to
accumulate the scattering intensity at a given angle. The data
collection scheme precludes the need to measure the intensity
profile across the radiation fan.
Once the raw diffraction data are collected, the data analysis may
be fully automated. The diffraction intensities of the swollen
films may be used to calculate the phase of the scattering
amplitude for a given diffraction peak by least squares analysis.
Once the phases are known, the relative electron densities can be
calculated for the lipid bilayer by a discrete Fourier transform.
The density can be normalized to the maximum density in the layer
for purposes of comparison with other bilayer systems.
In one embodiment, the lipid vesicles are incubated with a
candidate drug before centrifugation into the lamellar stack in
order to determine the hospitality of the lipid matrix for that
candidate. After centrifugation and angular dispersive x-ray
diffraction analysis, the bilayer system treated with a drug
candidate may be compared with the control standard; any
statistical difference in the electron density profile is an
indication that the drug is incorporated in the membrane. Further
analysis can be used to determine the localization. The interested
reader is directed to Mason and Trumbore, which is hereby
incorporated by reference, for further detail on the analysis of
drug localization.
Additional applications related to lipid research is the
possibility of using the angular dispersive x-ray as a method for
determination of drug/lipid compatibility in a combinatorial
process. The small sample spot size of the beam makes the angular
dispersive x-ray amenable to small area illumination, for example
on a sample tray containing a large number of samples.
Application to Epitaxial Film Structure Determination and Growth.
In another aspect of the invention, the angular dispersive x-ray
apparatus of the invention may be adapted for use in the rapid
elucidation of structure and lattice mismatch in epitaxial films.
With the growing variety of epitaxial methods to prepare epitaxial
and superlattice structures of metals, semiconductors and
insulators comes the increasing need to find efficient and rapid in
situ methods of monitoring and controlling the growth process. The
deficiencies of the prior art which have been discussed in the
Background of the Invention include imprecision due to wide
detector slits and complicated and time-consuming data collection
methods.
The apparatus and method of the present invention combine the
advantages of partial reciprocal space mapping with speed of data
collection. The present invention will permit data collection
concerning the lattice mismatch and superlattice period of a
growing epitaxial layer in times on the order of 1 second. The
invention may be configured in accordance with FIG. 1 to illuminate
a substrate with an epitaxial grown film at high angles
corresponding to diffraction which probes interatomic spacings. The
angular interval covered by the focusing optics is sufficient to
encompass diffraction from both the substrate, used for reference
purposes, and the epitaxial layer. X-rays from a conventional
copper x-ray tube may be simultaneously monochromatized and focused
onto the growing epitaxial layer. The monochromator is bent to
approximate a logarithmic spiral along the bending axis according
to the methodology described hereinabove. The monochromatic beam is
convergent on the sample within an envelop of .DELTA.(.OMEGA.) and
is simultaneously diffracted within an envelop of .DELTA.(2.OMEGA.)
onto a position sensitive detector. Typical values of the
.DELTA.(.OMEGA.) envelop may be about 2.degree., and the incident
angle of .OMEGA. about which the source is centered depends on the
reflection of interest and the constraints imposed by the
surrounding epitaxial equipment. The .OMEGA. may vary over a wide
range and may typically range from about 15.degree. to over
50.degree.. The only moving part is a slit positioned between the
x-ray source and the curved monochromator crystal. The slit may be
left open for dispersive, real time mode or narrowed for reciprocal
space mapping. The apparatus may optionally include in-situ
reciprocal space mapping capability. The system further may be
integrated into a conventional film deposition system, such a
metalorganic chemical vapor deposition (MOCVD) system or physical
vapor depositions systems, such as molecular beam epitaxy, laser
ablation, ion beam sputtering, reactive evaporation, e-beam
evaporation and the like.
This method is superior to conventional rocking curve approaches
since the diffraction intensities are measured simultaneously and
registered on a position-sensitive detector. Furthermore, due to
the rapid data collection, the diffractometer may be used to
accumulate diffraction intensities during deposition. The rapid
intensity determination may then be used to control the deposition
characteristics in order to control the film structure.
Surface Mapping. Because of the fine focusing characteristics of
this invention, x-ray diffraction may be performed on a lateral
scale on the order of microns, which is not currently feasible with
current laboratory x-ray sources. For further lateral resolution
perpendicular to the focusing plane, the invention may be equipped
with a focusing device perpendicular to the monochromator. Because
the diffraction is measured in the plane of incidence corresponding
to that of the monochromator, the alternate focusing may be
performed by a curved mirror, or another curved monochromator
(either synthetic multilayer or single crystal type).
Film Thickness Measurement. The invention may be used to measure
the thickness and density of thin films (up to about 200 nm in
thickness) by using the convergent x-ray beam from the
monochromator to illuminate a thin film covered substrate at
grazing incident angles (0-0.3.degree.) and measuring the x-ray
reflectivity on the position sensitive detector. One observes
interference maxima and minima as a function of angle and these can
be related directly to the film thickness and density by the
modified Bragg equation: ##EQU16## where .theta. is the angle at
which a maximum or minimum in the reflectivity occurs, .lambda. is
the x-ray wavelength, d is the film thickness and .delta. is the
real correction to the x-ray index of refraction; this term is on
the order of 10.sup.-6 and in a direction proportional to the film
density. N is used to index the maxima and minima in the
reflectivity, and will have the values 1, 2, 3 . . . for
.theta..sub.max. and 0.5, 1.5, 2.5, . . . for .theta..sub.min..
Because the x-ray reflectivity is measured simultaneously over a
range of angles, the data collection is orders of magnitude faster
than the conventional x-ray reflectivity scan, in which the
reflection intensity is measured one angle at a time. This makes it
possible to use the thickness derived from our invention to perform
real-time in situ control of film thickness as a part of a larger
deposition system. Film deposition systems which are known in the
art may be adapted to accommodate the thickness measuring apparatus
and method of the invention. The system may be integrated into a
conventional film depostition system, such a metalorganic chemical
vapor deposition (MOCVD) system or physical vapor depositions
systems, such as molecular beam epitaxy, laser ablation, ion beam
sputtering, reactive evaporation, e-beam evaporation and the like.
The interested reader is referred to Luken et al for further
information on the in situ growth monitoring of crystallographic
layers, which is hereby incorporated by reference.
* * * * *